A linear algorithm for embedding planar graphs using PQ-trees
Journal of Computer and System Sciences
Recognizing Leveled-Planar Dags in Linear Time
GD '95 Proceedings of the Symposium on Graph Drawing
Pitfalls of Using PQ-Trees in Automatic Graph Drawing
GD '97 Proceedings of the 5th International Symposium on Graph Drawing
Journal of Computer and System Sciences
An Approach for Mixed Upward Planarization
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Drawing Graphs on Two and Three Lines
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
On the Parameterized Complexity of Layered Graph Drawing
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Theoretical Computer Science
Graph Simultaneous Embedding Tool, GraphSET
Graph Drawing
Embeddability Problems for Upward Planar Digraphs
Graph Drawing
Characterization of unlabeled level planar trees
GD'06 Proceedings of the 14th international conference on Graph drawing
Characterization of unlabeled level planar graphs
GD'07 Proceedings of the 15th international conference on Graph drawing
Matched drawability of graph pairs and of graph triples
Computational Geometry: Theory and Applications
On the characterization of level planar trees by minimal patterns
GD'09 Proceedings of the 17th international conference on Graph Drawing
Toward a theory of planarity: hanani-tutte and planarity variants
GD'12 Proceedings of the 20th international conference on Graph Drawing
Crossing-constrained hierarchical drawings
Journal of Discrete Algorithms
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In a leveled directed acyclic graph G = (V,E) the vertex set V is partitioned into k 驴 |V| levels V1; V2,...,Vk such that for each edge (u, v) 驴 E with u 驴 i and v 驴 j we have i j. The level planarity testing problem is to decide if G can be drawn in the plane such that for each level i, all v 驴 i are drawn on the line li = {(x, k-i) | x 驴 R}, the edges are drawn monotone with respect to the vertical direction, and no edges intersect except at their end vertices. If G has a single source, the test can be performed in O(|V|) time by an algorithm of Di Battista and Nardelli (1988) that uses the PQ-tree data structure introduced by Booth and Lueker (1976). PQ-trees have also been proposed by Heath and Pemmaraju (1996a,b) to test level planarity of leveled directed acyclic graphs with several sources and sinks. It has been shown in J眉nger, Leipert, and Mutzel (1997) that this algorithm is not correct in the sense that it does not state correctly level planarity of every level planar graph. In this paper, we present a correct linear time level planarity testing algorithm that is based on two main new techniques that replace the incorrect crucial parts of the algorithm of Heath and Pemmaraju (1996a,b).